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Let's solve each problem shown in the image step-by-step.

### Problem 8

The triangle shown has two equal sides, indicated by the marks on the two sides, making it an **isosceles triangle**. In an isosceles triangle, the angles opposite the equal sides are also equal.

1. Let the two base angles be \((4x + 8)^\circ\) each.
2. Since the sum of angles in a triangle is \(180^\circ\), we can set up the equation:
   \[
   (4x + 8) + (4x + 8) + \text{vertex angle} = 180^\circ
   \]
3. Solving this equation will give the value of \(x\) and the angles.

However, from the image, it appears we only have one angle marked. Please confirm if the vertex angle or additional information is provided.

### Problem 10

In Problem 10, we also have an **isosceles triangle** with angles of \(29^\circ\) and \((11x - 65)^\circ\). 

1. The two angles opposite the equal sides are \((11x - 65)^\circ\) and \(29^\circ\).
2. Since the sum of angles in a triangle is \(180^\circ\), we can set up the equation:
   \[
   (11x - 65) + 29 + 29 = 180
   \]
3. Simplifying this equation will allow us to find the value of \(x\) and the angles.

Would you like me to proceed with the solutions for these equations, or would you like to provide any missing details? 

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Here are some related questions for practice:

1. How do you determine if a triangle is isosceles?
2. What is the significance of the sum of the angles in a triangle?
3. How do you set up equations when given expressions for angles in a triangle?
4. Why do the angles opposite equal sides in an isosceles triangle remain equal?
5. How would the solution change if one side of the triangle were different?

**Tip:** When working with triangles, always remember that the sum of all interior angles must equal 180 degrees.

Solve for x in the given isosceles triangles, where angles are expressed as algebraic expressions: (4x + 8)° and (11x - 65)°.

Learn how to solve for x in isosceles triangles with angles expressed as algebraic expressions: (4x + 8)° and (11x - 65)°. This problem includes algebraic expressions and the Base Angles Theorem, suitable for students in Grades 8-10.

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